如图(a)所示,在足够长的光滑水平面上,放置一长为L=1m、质量为m1=0.5kg的木板A,一质量为m2=1kg的小物体B以初速度v0滑上A的上表面的同时对A施加一个水平向右的力F,A与B之
◎ 题目
如图(a)所示,在足够长的光滑水平面上,放置一长为L=1m、质量为m1=0.5kg的木板A,一质量为m2=1kg的小物体B以初速度v0滑上A的上表面的同时对A施加一个水平向右的力F,A与B之间的动摩擦因数为μ=0.2,g=10m/s2;小物体B在A上运动的路程S与F力的关系如图(b)所示。求:v0、F1、F2。 |
◎ 答案
(1)4m/s;(2)3N;(3)9N |
◎ 解析
(1)由图象可看出当F≤1N时,B物体在A板上的路程始终等于板长L,当F=1N时,刚好不从A板右端掉下,此后A和B一起相对静止并加速运动。 设B物体的加速度为a2,A板的加速度为a1,分别由牛顿第二定律: μm2g=m2a2 ············································································································ ① F+μm2g=m1a1 ······································································································· ② 设B运动的位移为S2,A运动的位移为S1,经过t时间两者速度均为v,根据运动学公式: SB=t ············································································································· ③ SA=t ·················································································································· ④ v=v0-a2t=a1t········································································································· ⑤ B在A上相对A向右运动的路程S=SB-SA ······································································ ⑥ 联立①②③④⑤⑥解得:S=··············································································· ⑦ 将F=1N,S=1m代入,解得:v0=4m/s (2)根据⑦式分析可知,当1N≤F≤F1时,随着F力增大,S减小,当F=F1时,出现S突变,说明此时A、B在达到共同速度后,恰好再次发生相对运动,B将会从A板左端掉下。 对A、B恰好发生相对运动时,B的加速度为a2,则整体加速度也为a2,由牛顿第二定律: F1=(m1+m2)a2········································································································ ⑧ 联立①⑧解得解得F1=3N (3)此时B在A上运动的路程为S1==m 当F≥F1时,物体B在A板上的路程为B相对A向右运动的路程的两倍。 故当F=F2时,将S=0.5S1代入⑦式解得:F2=9N 【评析】本题考查牛顿运动定律。滑块问题是物理模型中非常重要的模型,是学生物理建模能力培养的典型模型。滑块问题的解决非常灵活,针对受力分析、运动分析以及牛顿第二定律的掌握,还有相对运动的分析,特别是摩擦力的变化与转型,都是难点所在。本题通过非常规的图象来分析滑块的运动,能从图中读懂物体的运动。 |
◎ 知识点
专家分析,试题“如图(a)所示,在足够长的光滑水平面上,放置一长为L=1m、质量为m1=0.5kg的木板A,一质量为m2=1kg的小物体B以初速度v0滑上A的上表面的同时对A施加一个水平向右的力F,A与B之…”主要考查了你对 【牛顿运动定律的应用】 等知识点的理解和应用能力。关于这些知识点的“档案”,你可以点击相应的链接进行查看和学习。- 最新内容
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